#!/usr/bin/env python
# coding: utf-8
# # Venus
#
# OK. Venus is at its maximum angular separation from the Sun when Earth-Venus-Sun [form a right triangle](https://en.wikipedia.org/wiki/Elongation)—which is when the Earth-Venus line-of-sight is tangent to the orbit of Venus...
#
#
# In[32]:
get_ipython().run_line_magic('matplotlib', 'inline')
import matplotlib.pyplot as plt
plt.style.use('seaborn-whitegrid')
import numpy as np
import pandas as pd
# In[33]:
theta = []
thetaprime = []
thetadiff = []
b = 0.723
pi = 3.141592653
for i in range(-500,500):
thetai = pi*i/1000
y = np.sin(thetai)
x = np.cos(thetai)
yprime = y - b
xprime = x
thetaprimei = np.arctan(yprime/xprime)
thetadiffi = thetai - thetaprimei
theta = theta + [thetai]
thetaprime = thetaprime + [thetaprimei]
thetadiff = thetadiff + [thetadiffi]
data = [('theta', theta),('thetaprime', thetaprime), ('thetadiff', thetadiff)]
venus = pd.DataFrame.from_items(data)
venus.plot()
# ## Venus
#
#
#
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